Looks like a "notorious" Fluidmaster. You can try replacing the rubber diaphragm seal under the plastic cover.
If you have the original box or a receipt, you can call them at 800-631-2011 and attempt to get them to ship you a replacement part for free. Where I live, the chlorine is bad and there are geckos in the water supply. No Fluidmaster fill valve is impervious to leaks. The above link is disabled for in-forum playback, but it will take you to a separate youtube window to play.